MATTER IN MOTION 107 



in which the helical space-time paths that we 

 have discussed are the nearest possible ap- 

 proach to straight lines. Strange as this new 

 geometry appears, it has been found to con- 

 form to experiment in the three crucial tests 

 which have so far been applied to it. 



As a navigator sailing farther and farther 

 from home makes observations and measure- 

 ments which tally less and less with the predic- 

 tions of the plane geometry of Euclid, so it is 

 assumed in the new theory of Einstein, which is 

 now being generally accepted, that the whole 

 phenomenon of gravitation can be interpreted 

 through the assumption that the flat geometry 

 which we have employed in the preceding chap- 

 ter does not quite lend itself to measurements 

 of space and time made in the immediate neigh- 

 borhood of a massive object. The departure 

 from "flatness" which must be assumed is, how- 

 ever, so extremely small that estimates of dis- 

 tance made by Euclidean methods near the 

 surface of the earth would never be in error by 

 more than one part in a thousand million, while 

 near the surface of the sun they might amount 

 to as much as two parts in a million. 



It was Clifford^ who first suggested that 



3 W. K. Clifford, Mathematical Papers. 



